Microscopes, like all image-forming optical instruments, have limited resolving ability (“resolution”) even if the optical components are made perfectly. The limited resolution is due to diffraction that occurs at the aperture stop or pupil of the instrument. This fundamental phenomenon was first explained in 1873, by Ernst Karl Abbe. Abbe explained that the smallest possible image that can be formed by a microscope objective has a spot radius r given by: r=(λ/2)·n·sin(θ), where r is the radius of the smallest possible spot, λ is the wavelength of the light used to form the image, n is the index of refraction of the medium containing the image and θ is the angle between the axis and the outermost ray forming the image in the medium containing the image.
The quantity n·sin(θ) is known as the numerical aperture (NA). Thus, the above equation can be rewritten as: r=λ/(2·NA).
If two points of equal intensity are observed through a microscope objective, then the minimum separation s that can be resolved is given by Abbe's formula: s=0.61λ/NA. This is also called the “Abbe limit.”
According to the Abbe formula, the resolving power of a microscope objective can be improved via the use of shorter wavelengths and/or a higher NA. However, the maximum value of the NA is limited by the index of refraction of available immersion liquids (oil and water being generally preferred) and the maximum value of the sine function, which is unity. In practice, the maximum value of NA is about 1.35. The shortest wavelength visible to the eye is about 0.43 microns, and for lithography the shortest wavelength currently in general use is a deep-UV, excimer-laser wavelength of 193 nm.
Using very complicated mask patterns and manipulating the angle and polarization of the incident light, as well as the relative phase of the light transmitted through the mask pattern, makes it possible to improve the resolution limit achieved in a lithography system beyond that predicted by Abbe by about a factor of less than 2. This is achieved only with great difficulty and under very special conditions. Diffraction is a fundamental part of image formation and cannot be avoided.